The Tigers have reached the last four of the competition for the first time since 1930 and only League One Sheffield United stand in their way of further progress.
Steve Bruce would be delighted if his side can focus on their trip to Wembley next weekend having extinguished the minor doubts still surrounding their Premier League safety.
Hull are seven points clear of the relegation zone having avoided the bottom end of the table for much of their first season back in the top flight, but probably need one more win to guarantee survival.
Interim Swans boss Garry Monk has admitted this week that the club will look to bring the Dutchman to Wales on a permanent deal in the summer following the conclusion of his second season-long loan spell.
Whether Monk will be in charge next season, though, is still up in the air and so the 34-year-old will be determined to finish the season strongly to stake his claim to be given the manager's role full time.
He has only one senior injury worry to contend with, as Kyle Bartley remains on the sidelines with a hamstring strain, and so could name the same side that were convincing victors over the Canaries.
Michu, their 19-goal top scorer from last season, is working his way back to full fitness after ankle surgery forced him to miss three months of action and should slot in behind striker Wifried Bony.
The Ivorian has already netted 20 times in his debut campaign at the Liberty Stadium and is thought to be garnering interest from other clubs in the division, including Champions League-chasing Everton.
Hull will continue to be without goalkeeper Allan McGregor, who has joined Paul McShane and Robbie Brady on the long-term injury list after suffering kidney damage in the 2-1 defeat to West Ham United.
George Boyd is available again for the Tigers after completing his three-match suspension for spitting at Manchester City's Joe Hart, and will probably be named on the bench as Bruce sticks with his settled side.
Ahmed Elmohamady made a costly error at the Britannia Stadium, but is the only Hull player to have started every Premier League game this season and should be kept faith with again.
Possible starting lineups
Hull: Harper; Rosenior, Davies, Chester, Figueroa, Elmohamady; Huddlestone, Meyler, Livermore; Long, Jelavic
Swansea: Vorm; Rangel, Chico, Williams, Davies; Britton, Shelvey; De Guzman, Michu, Routledge; Bony
Sports Mole says: 1-1